The Propagation Properties of a Laguerre–Gaussian Beam in Nonlinear Plasma

The self-focusing properties of the Laguerre-Gaussian (LG) beam in nonlinear plasma, characterized by significant collisional or ponderomotive nonlinearity have been explored. The second-order differential equation of the beam width is established from Maxwell’s equations with Wentzel–Kramers–Brillouin (WKB) and paraxial like approximation. The effect of the vortex charge number, intensity parameter and plasma temperature on the self-focusing properties of the Laguerre-Gaussian beam has been investigated.

Focusing properties and focal shift of vortex Hermite-cosh- Gaussian beams

In this work, we investigate the focusing properties of a vortex Hermite-cosh-Gaussian beam (vHChGB) passing through a converging lens system. The analytical propagation equation as well as the beam width expression of a focused vHChGB is derived based on the Huygens-Fresnel diffraction principle. From the obtained formulae, the effects of the Gaussian Fresnel number NF and the beam parameters on the structure of the light intensity distribution and the beam spot size in the focal region are analyzed numerically. It is shown that the focal shift, which is determined from the minimum beam spot width criterion, is affected strongly by the change of the Fresnel number, the parameter b, and it is slightly altered by the vortex charge M and nearly insensitive to the beam order n. For a fixed value of NF, the focal shift is smaller when the parameter b or the vortex charge M is larger. The focal shift decreases monotonously with the increase of Fresnel number until it vanishes asymptotically for large NF. The obtained results may be useful for the applications of the vHChGBs in beam shaping and beam focusing.

Hall anomaly and moving vortex charge in layered superconductors

Magnetotransport theory of layered superconductors in the flux flow steady state is revisited. Longstanding controversies concerning observed Hall sign reversals are resolved. The conductivity separates into a Bardeen-Stephen vortex core contribution, and a Hall conductivity due to moving vortex charge. This charge, which is responsible for Hall anomaly, diverges logarithmically at weak magnetic field. Its values can be extracted from magetoresistivity data by extrapolation of vortex core Hall angle from the normal phase. Hall anomalies in YBa_22Cu_33O_{7}7, Bi_22Sr_22CaCu_22O_{8-x}8−x, and Nd_{1.85}1.85Ce_{0.15}0.15CuO_{4-y}4−y data are consistent with theoretical estimates based on doping dependence of London penetration depths. In the appendices, we derive the Streda formula for the hydrodynamical Hall conductivity, and refute previously assumed relevance of Galilean symmetry to Hall anomalies.